The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  0
 0  0  X  0  0  0  0  0  0  0  0  0
 0  0  0  X  0  0  0  0  0  0  0  0
 0  0  0  0  X  0  0  0  0  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  0
 0  0  0  0  0  0  0  X  0  0  0  0
 0  0  0  0  0  0  0  0  X  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  0
 0  0  0  0  0  0  0  0  0  0  X  0
 0  0  0  0  0  0  0  0  0  0  0  X

generates a code of length 12 over Z2[X]/(X^2) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+12x^2+66x^4+220x^6+495x^8+792x^10+5020x^12+792x^14+495x^16+220x^18+66x^20+12x^22+1x^24

The gray image is a linear code over GF(2) with n=24, k=13 and d=2.
This code was found by Heurico 1.16 in 0.0945 seconds.